ABSTRACT

We use multiscaling function interpolation method to solve the Dirich­ let problem via the wavelet Galerkin approach. We present convergence theory for the approximation of multiscaling function interpolation on a domain in R2 and provide a simplification in calculating the bound­ ary integrals. It is shown that our multiscaling function interpolation method provides more accurate approximate solutions of the Dirichlet problem than scalar scaling function interpolation methods.